Accurate eigenvalues of bounded oscillators

TL;DR

This paper introduces a highly accurate method for calculating eigenvalues of bounded oscillators using the Riccati–Padé approach, which employs rational approximations and Hankel determinants for rapid convergence.

Contribution

The paper presents a novel application of the Riccati–Padé method with Hankel determinants to achieve precise eigenvalues for bounded oscillators, improving convergence speed.

Findings

Sequences of roots approach eigenvalues from below

Remarkable convergence rate observed

Method outperforms previous techniques

Abstract

We calculate accurate eigenvalues of a bounded oscillator by means of the Riccati--Pad\'e method that is based on a rational approximation to a regularized logarithmic derivative of the wavefunction. Sequences of roots of Hankel determinants approach the model eigenvalues from below with remarkable convergence rate.